Chapter 7: Q. 37 (page 652)

In the following exercises, multiply the rational expressions.
$\frac{28 - 4 b}{3 b - 3} . \frac{b^{2} + 8 b - 9}{b^{2} - 49}$

Short Answer

Expert verified

The multiplication of the expressions is $\frac{- 4 (b + 9)}{(b + 7)} .$

Step by step solution

Step 1. Given information

The rational expression is $\frac{28 - 4 b}{3 b - 3} . \frac{b^{2} + 8 b - 9}{b^{2} - 49}$

Step 2. Factor each numerator and denominator completely.

Factor $28 - 4 b$ and $b^{2} - 49 .$

$28 - 4 b = 4 (7 - b)$ and

$b^{2} - 49 = (b - 7) (b + 7)$ and

$b^{2} + 8 b - 9 = b^{2} + 9 b - b - 9 = b (b + 9) - 1 (b + 9) = (b + 9) (b - 1)$

Step 3. Multiply the numerators and denominators.

$\frac{28 - 4 b}{3 b - 3} . \frac{b^{2} + 8 b - 9}{b^{2} - 49} = \frac{4 (7 - b)}{3 (b - 1)} . \frac{(b + 9) (b - 1)}{(b - 7) (b + 7)} = \frac{- 4 (b - 7) (b + 9)}{(b - 7) (b + 7)} = \frac{- 4 (b + 9)}{(b + 7)} .$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, multiply the rational expressions.
$\frac{28 - 4 b}{3 b - 3} . \frac{b^{2} + 8 b - 9}{b^{2} - 49}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Factor each numerator and denominator completely.

Step 3. Multiply the numerators and denominators.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Decision Maths

Pure Maths

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, multiply the rational expressions.28-4b3b-3.b2+8b-9b2-49

Short Answer

Step by step solution

Step 1. Given information

Step 2. Factor each numerator and denominator completely.

Step 3. Multiply the numerators and denominators.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Decision Maths

Pure Maths

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, multiply the rational expressions.
$\frac{28 - 4 b}{3 b - 3} . \frac{b^{2} + 8 b - 9}{b^{2} - 49}$